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Exponents

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  • 1.  Exponents represent repeated multiplication. For example,
  • 2.  More generally, for any non-zero real number a and for any whole number n,In the exponential expression an, a is calledthe base and n is called the exponent.
  • 3.  a2 is read as ‘a squared’. a3 is read as ‘a cubed’. a4 is read as ‘a to the fourth power’. ... an is read as ‘a to the nth power’.
  • 4. Homework.
  • 5. Homework.
  • 6. Homework.
  • 7. Homework.
  • 8. 1. All powers of a positive real number a are positive, i.e. for a ∈ R, a > 0, and n ∈ Z, an> 0.2. The even powers of a negative real numbera are positive, i.e. for a ∈ R, a ≠ 0 and n ∈ Z, (–a)n = an (if n is an even number).3. The odd powers of a negative real number aare negative, i.e. for a ∈ R, a ≠ 0 and n ∈ Z, (–a)n= –an (if n is an odd number)
  • 9. The terms of an expression which have the same base and the same exponent are called like terms. We can add or subtract like terms.(x ⋅ an) + (y ⋅ an) + (z ⋅ an) = (x + y + z) ⋅ an (a ≠ 0)
  • 10.  Let a ∈ R – {–1, 0, 1}(a is a real number other than –1, 0 and 1). If am = an then m = n.
  • 11.  2x = 16 3x+1 = 81 22x + 1 = 8x – 1